Molecular dynamics computer simulations of octylglucoside (OG) micelles over a range of aggregation number from 5 to 100 were analyzed for their dynamical behavior and the results compared with NMR relaxation measurements. While agreement experimental data was good (signifying appropriate simulation methodology), it was found that previously published interpretations from other laboratories were incorrect. The simulations demonstrated that lateral diffusion of the individual lipids, rather than rotation of the entire micelle, dominates the long time decay. This finding has important implications for determining micelle structure from NMR. Langevin dynanmics simulations were carried out on the pentassaccharide lacto-N-fucopentaose-1 in a successful effort to interpret NMR measurements. A combined approach based on simulation, hydrodynamic calculations and analytic theory showed that large internal flexibility of the terminal region, rather than molecular anisotropy, was leading to the unusual pattern of relaxation data. Molecular dynamics simulations of gel phase of DPPC were finally completed. Of particular note was the slow isomerization of torsion 1 of chain 2, which provides explainations of the seemingly anomalous IR results for gauche bonds in the upper region of the chains, and the very long time required to recrystallize this phase.